Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SA-SUPPLEMENT SUBMODULES

  • Received : 2020.02.09
  • Accepted : 2020.09.15
  • Published : 2021.01.31
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Abstract

In this paper, we introduced and studied sa-supplement submodules. A submodule U of a module V is called an sa-supplement submodule in V if there exists a submodule T of V such that V = T + U and U ∩ T is semiartinian. The class of sa-supplement sequences ������ is a proper class which is generated by socle-free modules injectively. We studied modules that have an sa-supplement in every extension, modules whose all submodules are sa-supplement and modules whose all sa-supplement submodules are direct summand. We provided new characterizations of right semiartinian rings and right SSI rings.

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References

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